Distance formulas on weighted Banach spaces of analytic functions

[EN] Let v be a radial weight function on the unit disc or on the complex plane. It is shown that for each analytic function f0 in the Banach space Hv all analytic functions f such that v|f| is bounded, the distance of f0 to the subspace Hv0 of Hv of all the functions g such that v|g| vanishes at in...

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Detalhes bibliográficos
Autores: Bonet Solves, José Antonio|||0000-0002-9096-6380, Lusky, Wolfgang, Taskinen, Jari
Formato: artículo
Fecha de publicación:2019
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/155435
Acesso em linha:https://riunet.upv.es/handle/10251/155435
Access Level:acceso abierto
Palavra-chave:Banach spaces of analytic functions
Weight
Distance
Bloch functions
MATEMATICA APLICADA
Descrição
Resumo:[EN] Let v be a radial weight function on the unit disc or on the complex plane. It is shown that for each analytic function f0 in the Banach space Hv all analytic functions f such that v|f| is bounded, the distance of f0 to the subspace Hv0 of Hv of all the functions g such that v|g| vanishes at infinity is attained at a function g0Hv0. Moreover a simple, direct proof of the formula of the distance of f to Hv0 due to Perfekt is presented. As a consequence the corresponding results for weighted Bloch spaces are obtained.